Question: State Bragg Law. What assumptions were made while deriving Bragg equation?
Answer:
Bragg diffraction occurs when electromagnetic
radiation or waves with wavelength
comparable to atomic spacings are incident
upon a crystalline sample and are scattered in
a specular fashion by the atoms in the system,
and undergo constructive interference. For a
crystalline solid, the waves are scattered from
lattice planes separated by the interplanar
distance d. Where the scattered waves
interfere constructively, they remain in phase
since the path length of each wave is equal to an integer multiple of the wavelength.
Suppose that a single monochromatic wave (of any type) is incident on aligned planes of lattice
points, with separation , at angle . Points A and C are on one plane, and B is on the plane
below. Points ABCC' form a quadrilateral. There will be a path difference between the ray that
gets reflected along AC' and the ray that gets transmitted, then reflected, along AB and BC
respectively. This path difference is
The two separate waves will arrive at a point with the same phase, and hence undergo
constructive interference, if and only if this path difference is equal to any integer value of the
wavelength, i.e.
where the same definition of and
Therefore,
apply as above.
and
from which it follows that
Putting everything together,
which is Bragg's law.
which simplifies to
Assumptions:
1) Falling light is a single monochromatic wave
2) If only two planes of atoms were diffracting, then the transition from constructive to destructive
interference would be gradual as the angle is varied.
3) Grating is periodic